Problem $4\mathrm{.}4$

Imagine that Penn State is trimming branches from a tree. As the workers are lowering a $30$ kg branch at

a constant rate of $0\mathrm{.}16\frac{m}{s},$ a student cuts through the work zone so the workers suddenly stop lowering

the branch. The rope $($modulus of elasticity $E=2\mathrm{.}6$GPa $)$ supporting the branch has a diameter of $4$ cm

and a damping constant of $1510N*\frac{s}{m}.$ The rope has a length of $2\mathrm{.}7$ m when it is stopped. Find the response

of the system numerically assuming that $x$ is positive up$.$

Answer: